On Pedal and Contrapedal Curves of Bézier Curves

Year 2021, Volume: 9 Issue: 2, 217 - 221, 15.10.2021

Ayşe Yılmaz Ceylan , Merve Kara

Abstract

The aim of this paper is to charaterize pedal and contrapedal curves of a Bézier curve which has many applications in computer graphics and related areas. Moreover, the pedal and contrapedal curve of a planar Bézier curve at the starting and the ending points are investigated.

Keywords

Bezier curve, Contrapedal curve, Pedal curve

References

• 1) Do Carmo, M. P., \textit{Differential Geometry of Curves and Surfaces}, Prentice-Hall, Englewood Cliffs, NJ, 1976.
• 2) Erkan, E. and Yüce, S., Serret-Frenet Frame and Curvatures of Bézier Curves, Mathematics, Vol:6, No.12 (2018), 321, 1-20.
• 3) Gray, A., Abbena, E. and Salamon, S., \textit{Modern Differential Geometry of Curves and Surfaces with Mathematica}, Chapman and Hall/CRC: Boca Raton, FL, USA, 2016.
• 4) Li Y, Pei D. Pedal curves of frontals in the Euclidean plane, Math. Meth. Appl. Sci., 41, (2018), 1988–1997.
• 5) Marsh, D., \textit{Applied geometry for computer graphics and CAD}, Springer, 2006.
• 6) O'Neill, B., \textit{Elemantary Differential Geometry}, Academic Oress, Rev. 2nd.ed., Elsevier, USA, 2006.
• 7) Tuncer OO, Ceyhan H, Gök İ, Ekmekci FN. Notes on pedal and contrapedal curves of fronts in the Euclidean plane, Math. Meth. Appl. Sci., 41, (2018), 5096–5111.